def __init__(self, theory, constrains, title='', prompt=''):
self.theory = theory
self.constrains = list(constrains)
self.s = z3.Solver()
self.s.add(clauses_to_z3(self.theory))
self.alits = [
z3.Const('__core_aux{}'.format(n), z3.BoolSort())
for n, c in enumerate(self.constrains)
]
for a, c in zip(self.alits, self.constrains):
self.s.add(z3.Or(z3.Not(a), ivy_solver.formula_to_z3(c)))
options = OrderedDict(
(str(c), n) for n, c in enumerate(self.constrains))
self.select = widgets.SelectMultiple(options=options, value=[])
self.prompt = widgets.Latex(prompt)
self.result = widgets.Latex('')
self.check_button = widgets.Button(description='Check SAT')
self.check_button.on_click(self.check)
super(UserSelectCore, self).__init__(title, [
self.prompt,
self.select,
self.check_button,
self.result,
])
def __init__(self, theory, constrains, title="", prompt=""):
self.theory = theory
self.constrains = list(constrains)
self.s = z3.Solver()
self.s.add(clauses_to_z3(self.theory))
self.alits = [z3.Const("__core_aux{}".format(n), z3.BoolSort()) for n, c in enumerate(self.constrains)]
for a, c in zip(self.alits, self.constrains):
self.s.add(z3.Or(z3.Not(a), ivy_solver.formula_to_z3(c)))
options = OrderedDict((str(c), n) for n, c in enumerate(self.constrains))
self.select = widgets.SelectMultiple(options=options, value=[])
self.prompt = widgets.Latex(prompt)
self.result = widgets.Latex("")
self.check_button = widgets.Button(description="Check SAT")
self.check_button.on_click(self.check)
super(UserSelectCore, self).__init__(title, [self.prompt, self.select, self.check_button, self.result])
# globals are the inflexible symbols
gsyms = [ns(sym) for sym in inflex]
print "lsyms = {}".format(lsyms)
print "gsyms = {}".format(gsyms)
init = state.clauses
init = forward_clauses(init, inflex)
print "init = {}".format(init)
error = forward_clauses(error, inflex)
print "error = {}".format(error)
axioms += forward_clauses(axioms, inflex)
init_z3 = sv.clauses_to_z3(init)
print "init_z3 = {}".format(init_z3)
for a in updates:
print lu.simplify_clauses(a[1])
rho_z3 = z3.Or(
*[sv.clauses_to_z3(lu.simplify_clauses(a[1])) for a in updates])
print "rho_z3 = {}".format(rho_z3)
bad_z3 = sv.clauses_to_z3(error)
print "bad_z3 = {}".format(bad_z3)
background_z3 = sv.clauses_to_z3(axioms)
print "background_z3 = {}".format(background_z3)
#relations_z3 = [ns(rel) for rel in sig.relations if tr.is_new(rel) or rel in inflex]
relations_z3 = [
x for x in gsyms
if not z3.is_const(x) or (z3.is_const(x) and x.sort() == z3.BoolSort())
]
def interactive_updr():
frames = ta._ivy_ag.states
if len(frames) != 1:
raise InteractionError(
"Interactive UPDR can only be started when the ARG " +
"contains nothing but the initial state.")
bad_states = negate_clauses(ta.get_safety_property())
action = ta.get_big_action()
ta._ivy_ag.actions[repr(action)] = action
init_frame = last_frame = frames[0]
# TODO: test conjecture in initial
while True:
# the property is true in all frames and all "clauses" are pushed
# the goal stack is empty
# check if we found an infuctive invariant
for i in range(len(frames) - 1):
if t.check_cover(frames[i + 1], frames[i]):
ta.step(msg="Inductive invariant found at frame {}".format(i),
i=i)
# return True
# add new frame
last_frame = ta.arg_add_action_node(last_frame, action, None)
ta.push_goal(ta.goal_at_arg_node(bad_states, last_frame))
ta.step(msg="Added new frame")
# push facts to last frame
t.recalculate_facts(last_frame,
ta.arg_get_conjuncts(ta.arg_get_pred(last_frame)))
while True:
current_goal = ta.top_goal()
if current_goal is None:
# goal stack is empty
break
if t.remove_if_refuted(current_goal):
continue
if current_goal.node == init_frame:
# no invariant
print "No Invariant!"
# return False
dg = ta.get_diagram(current_goal, False)
options = OrderedDict()
for c in simplify_clauses(dg.formula).conjuncts():
options[str(c)] = c
user_selection = (yield UserSelectMultiple(
options=options,
title="Generalize Diagram",
prompt="Choose which literals to take as the refutation goal",
default=options.values()))
assert user_selection is not None
ug = ta.goal_at_arg_node(Clauses(list(user_selection)),
current_goal.node)
ta.push_goal(ug)
ta.step(msg='Pushed user selected goal', ug=ug)
goal = ta.top_goal()
preds, action = ta.arg_get_preds_action(goal.node)
assert action != 'join'
assert len(preds) == 1
pred = preds[0]
axioms = ta._ivy_interp.background_theory()
theory = and_clauses(
ivy_transrel.forward_image(pred.clauses, axioms,
action.update(ta._ivy_interp,
None)), axioms)
goal_clauses = simplify_clauses(goal.formula)
assert len(goal_clauses.defs) == 0
s = z3.Solver()
s.add(clauses_to_z3(theory))
s.add(clauses_to_z3(goal_clauses))
is_sat = s.check()
if is_sat == z3.sat:
bi = ta.backward_image(goal.formula, action)
x, y = False, ta.goal_at_arg_node(bi, pred)
elif is_sat == z3.unsat:
user_selection, user_is_sat = yield UserSelectCore(
theory=theory,
constrains=goal_clauses.fmlas,
title="Refinement",
prompt="Choose the literals to use",
)
assert user_is_sat is False
core = Clauses(user_selection)
x, y = True, ivy_transrel.interp_from_unsat_core(
goal_clauses, theory, core, None)
else:
assert False, is_sat
t.custom_refine_or_reverse(goal, x, y, False)
# propagate phase
for i in range(1, len(frames)):
facts_to_check = (set(ta.arg_get_conjuncts(frames[i - 1])) -
set(ta.arg_get_conjuncts(frames[i])))
t.recalculate_facts(frames[i], list(facts_to_check))
# globals are the inflexible symbols
gsyms = [ns(sym) for sym in inflex]
print "lsyms = {}".format(lsyms)
print "gsyms = {}".format(gsyms)
init = state.clauses
init = forward_clauses(init,inflex)
print "init = {}".format(init)
error = forward_clauses(error,inflex)
print "error = {}".format(error)
axioms += forward_clauses(axioms,inflex)
init_z3 = sv.clauses_to_z3(init)
print "init_z3 = {}".format(init_z3)
for a in updates:
print lu.simplify_clauses(a[1])
rho_z3 = z3.Or(*[sv.clauses_to_z3(lu.simplify_clauses(a[1])) for a in updates])
print "rho_z3 = {}".format(rho_z3)
bad_z3 = sv.clauses_to_z3(error)
print "bad_z3 = {}".format(bad_z3)
background_z3 = sv.clauses_to_z3(axioms)
print "background_z3 = {}".format(background_z3)
#relations_z3 = [ns(rel) for rel in sig.relations if tr.is_new(rel) or rel in inflex]
relations_z3 = [ x for x in gsyms if not z3.is_const(x) or (z3.is_const(x) and x.sort() == z3.BoolSort()) ]
relations_z3 += [ x for _,x in lsyms if not z3.is_const(x) or (z3.is_const(x) and x.sort() == z3.BoolSort()) ]
print "relations_z3 = {}".format(relations_z3)
### HACK: remove skolem predicates from the list of predicate symbols
def interactive_updr():
frames = ta._ivy_ag.states
if len(frames) != 1:
raise InteractionError(
"Interactive UPDR can only be started when the ARG " + "contains nothing but the initial state."
)
bad_states = negate_clauses(ta.get_safety_property())
action = ta.get_big_action()
ta._ivy_ag.actions[repr(action)] = action
init_frame = last_frame = frames[0]
# TODO: test conjecture in initial
while True:
# the property is true in all frames and all "clauses" are pushed
# the goal stack is empty
# check if we found an infuctive invariant
for i in range(len(frames) - 1):
if t.check_cover(frames[i + 1], frames[i]):
ta.step(msg="Inductive invariant found at frame {}".format(i), i=i)
# return True
# add new frame
last_frame = ta.arg_add_action_node(last_frame, action, None)
ta.push_goal(ta.goal_at_arg_node(bad_states, last_frame))
ta.step(msg="Added new frame")
# push facts to last frame
t.recalculate_facts(last_frame, ta.arg_get_conjuncts(ta.arg_get_pred(last_frame)))
while True:
current_goal = ta.top_goal()
if current_goal is None:
# goal stack is empty
break
if t.remove_if_refuted(current_goal):
continue
if current_goal.node == init_frame:
# no invariant
print "No Invariant!"
# return False
dg = ta.get_diagram(current_goal, False)
options = OrderedDict()
for c in simplify_clauses(dg.formula).conjuncts():
options[str(c)] = c
user_selection = (
yield UserSelectMultiple(
options=options,
title="Generalize Diagram",
prompt="Choose which literals to take as the refutation goal",
default=options.values(),
)
)
assert user_selection is not None
ug = ta.goal_at_arg_node(Clauses(list(user_selection)), current_goal.node)
ta.push_goal(ug)
ta.step(msg="Pushed user selected goal", ug=ug)
goal = ta.top_goal()
preds, action = ta.arg_get_preds_action(goal.node)
assert action != "join"
assert len(preds) == 1
pred = preds[0]
axioms = ta._ivy_interp.background_theory()
theory = and_clauses(
ivy_transrel.forward_image(pred.clauses, axioms, action.update(ta._ivy_interp, None)), axioms
)
goal_clauses = simplify_clauses(goal.formula)
assert len(goal_clauses.defs) == 0
s = z3.Solver()
s.add(clauses_to_z3(theory))
s.add(clauses_to_z3(goal_clauses))
is_sat = s.check()
if is_sat == z3.sat:
bi = ta.backward_image(goal.formula, action)
x, y = False, ta.goal_at_arg_node(bi, pred)
elif is_sat == z3.unsat:
user_selection, user_is_sat = yield UserSelectCore(
theory=theory,
constrains=goal_clauses.fmlas,
title="Refinement",
prompt="Choose the literals to use",
)
assert user_is_sat is False
core = Clauses(user_selection)
x, y = True, ivy_transrel.interp_from_unsat_core(goal_clauses, theory, core, None)
else:
assert False, is_sat
t.custom_refine_or_reverse(goal, x, y, False)
# propagate phase
for i in range(1, len(frames)):
facts_to_check = set(ta.arg_get_conjuncts(frames[i - 1])) - set(ta.arg_get_conjuncts(frames[i]))
t.recalculate_facts(frames[i], list(facts_to_check))